I\'ve seen some discussions on SO regarding $(this) vs $this in jQuery, and they make sense to me. (See discussion here for an example.)
Bu
You usually use var $this = $(this); to avoid creating a new jQuery object more often than necessary. In case of the code below you only create one object instead of two/four. It is completely unrelated to chainability.
You could also call it that, $thi$ or anything else (don't use the latter one though, it's ugly :p) as $ is just a simple character in JavaScript, exactly like a-z are.
Inside $.fn.lockDimensions, this is the jQuery object that had lockDimensions called on it.
Inside the .each, this now references the DOMElement in the current iteration of the loop. $(this) wraps the DOMElement in a jQuery object, and var $this = $(this); is just saving $(this) in a variable called $this, so the jQuery constructor doesn't need to be called multiple times (if you were to use $(this) instead).
$this = $(this)
which means that you are assigning the current object to a variable named $this. It is not a keyword.
It is just a variable name.